SOLUTION: If tan A = ¾ and cos B = 12/13, find a. Tan (A - B) b. c. tan ( B - A ) c. Sin ( A + B) d. cos 2A

Algebra ->  Trigonometry-basics -> SOLUTION: If tan A = ¾ and cos B = 12/13, find a. Tan (A - B) b. c. tan ( B - A ) c. Sin ( A + B) d. cos 2A      Log On


   

Question 1194315: If tan A = ¾ and cos B = 12/13, find
a. Tan (A - B)
b. c. tan ( B - A )
c. Sin ( A + B)
d. cos 2A
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If tan A = ¾ and cos B = 12/13, find
a. Tan (A - B)
b. c. tan ( B - A )
c. Sin ( A + B)
d. cos 2A
----------------
tan(A) = 3/4
tan = y/x
r = sqrt(x^2 + y^2) = 5
-----
sin = y/r
cos = x/r
cot = 1/tan
sec = 1/cos
csc = 1/sin
----
cos(B) = 12/13 = x/r ---> y = 5
sin = y/r
cos = x/r
tan = y/x
cot = 1/tan
sec = 1/cos
csc = 1/sin
=================
a. Tan (A - B)
b. c. tan ( B - A )
c. Sin ( A + B)
d. cos 2A
-----
Look up formulas at Wikipedia "Half angle formulas"
---- Email via the TY note for help or to check your work.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
If tan A = ¾ and cos B = 12/13, find
a. Tan (A - B)
b. c. tan ( B - A )
c. Sin ( A + B)
d. cos 2A
           matrix%281%2C7%2C+tan+%28A%29%2C+%22=%22%2C+O%2FA%2C+%22=%22%2C+3%2F4%2C+%22=%22%2C+y%2Fx%29                  
This is a 3-4-5 Pythag. Triple,    This is a 5-12-13 Pythag. Triple,
      so hypotenuse = H = r = 5    so opposite = O = y = 5   
Therefore,     Therefore, 

a. 
    Make the necessary substitutions and you should have the answer.

b. 
    Make the necessary substitutions and you should have the answer, 
    or
    Simply NEGATE a.

c. sin (A + B) = sin (A) cos (B) + cos (A) sin (B)
    Make the necessary substitutions and you should have the answer.

d. 
    Make the necessary substitutions and you should have the answer.